The equilibrium states of Cuntz-Pimsner type C*-algebras have been studied for several decades, with early work of Olesen and Pedersen illuminating the case of the Cuntz C*-algebra O_n. For the Toeplitz-Pimsner C*-algebra T_X associated to a C*-correspondence X over a coefficient algebra A there is a characterisation of an equilibrium (or Kubo-Martin-Schwinger) state at value beta, a real parameter, in terms of a subinvariance inequality on the trace on L(X) induced from a finite trace tau on A. Product systems over a cancellative monoid P generalise the single X to a semigroup of C*-correspondences. For the suitably defined Nica-Toeplitz algebra NT_X, it is possible to characterise an equilibrium state at beta by means of a system of inequalities expressing a certain positivity condition on induced traces in various fibres of X over P. I will present this general characterisation and discuss in more detail the case when P is an Artin monoid. The talk is based on joint works with Z. Afsar, S. Neshveyev, L. Gazdag, M. Laca.